Investment Performance Guy has a post “Periodicity of risk statistcs (and other measures)” in which it is wondered how valid volatility estimates are from a month of daily returns.
Here is a quick look. Figure 1 shows the variability (and a 95% confidence interval) of volatility estimates for the S&P 500 index in January 2011. Figure 2 is for the first quarter and Figure 3 is for the first half. All of these are with daily data.
The bootstrapping is done like:
for(i in 1:1e4) spxvolQ1.boot[i] <- sd(spxret11Q1[sample(62,62, replace=TRUE)])
The plots are something like: